A mechanical oscillator is a device that allows the movement of a weight to be maintained in relation to a stable point, under the effect of a force. The instantaneous force applied by the mechanical oscillator on the weight depends on several parameters, including the stiffness of the material of which the mechanical oscillator is composed. The mechanical oscillator is conventionally composed of a strip that can take a large variety of forms, such as a straight segment, a helicoid or a spiral.
Certain precision applications, such as the spiral springs intended to equip the rocker arm of a mechanical clockwork assembly, require a strip in the form of a spiral of which the stiffness varies as little as possible as a function of temperature. The stiffness of a spring of spiral type is defined by:
  K  =      M    φ  
where:
φ, the angle of twisting of the spring, and
M, the return torque of the spiral spring.
The equation for this return torque for a strip composed of a specific material is defined by:
  M  =      E          L      ⁡              (                                                            w                3                            ⁢              t                        12                    ⁢          φ                )            
where:
E is the Young's modulus of the material employed for the strip;
L is the length of the strip;
w is the width of the strip; and
t is the thickness of the strip.
The specific frequency of resonance of the spiral is proportional to the square root of its stiffness. Consequently, the frequency of the spiral is proportional to the square root of the Young's modulus of the material of the strip. Thus, if the Young's modulus varies as a function of temperature, the frequency of the spiral will also vary as a function of temperature. With a low variation in temperature, the frequency of the spiral therefore depends on the first order of variation in temperature of the Young's modulus. It is thus acknowledged that the following equation shows the variations in Young's modulus as a function of temperature:E=E0(1+∝E(T−T0))
where:
∝E is the thermal coefficient of the Young's modulus;
E is the Young's modulus at the temperature T, and
E0 is the Young's modulus at the temperature T0.
It is known to manufacture mechanical oscillators using alloys that are complex, both in terms of the number of components (iron, carbon, nickel, chrome, tungsten, molybdenum, beryllium, niobium, etc.), and in terms of the metallurgical processes used to obtain an auto-compensation of variations in the modulus of elasticity of the metal, by combining two contrary influences such as that of temperature and that of the magneto-constriction (contraction of magnetic objects under the effect of magnetization). However, these metal oscillators are difficult to manufacture. First of all, this is because of the complexity of the processes used for producing the alloys; the intrinsic mechanical properties of the metal are not constant from one production run to another. Additionally, the adjustment—which is the technique enabling one to ensure that the oscillator is regular—is fastidious and slow.
This operation requires many manual actions, and many defective parts have to be discarded. For these reasons, production is costly and maintaining constant quality is an ongoing challenge.
It is also known to produce mechanical oscillators by engraving a silicon wafer, to improve the regularity and precision of design. The processes for producing such mechanical oscillators generally use monocrystalline silicon wafers. Therefore, these mechanical oscillators have a monocrystalline direction that is predetermined by the silicon wafer used—for instance, all <100> directions. However, the Young's modulus of monocrystalline silicon is not the same in all the directions of the material, and this gives rise to a difference of mechanical behavior according to the axis of movement.
Swiss patent application no 699 780 concerns a mechanical oscillator of spiral type, produced from a monocrystalline silicon wafer. The temperature variations of the Young's modulus of the spiral-form strip are compensated by two amorphous layers located within the silicon strip, and of which the thermal coefficient of the Young's modulus is opposed to that of the silicon. This document does not compensate the temperature variations of the Young's modulus in the same way in multiple directions of the plane of the monocrystalline silicon wafer.
European patents no 1 422 436 and no 2 215 531 also address a mechanical oscillator of spiral type produced from a monocrystalline silicon wafer. The temperature variations of the Young's modulus are compensated by a layer of amorphous silicon oxide wrapped around a silicon strip. The thermal coefficient of the Young's modulus for silicon is −64·10-6K-1, and the thermal coefficient of the Young's modulus for silicon oxide is 187.5·10-6K-1 at an ambient temperature of around 20° C.
European patent no 1 422 436 proposes compensating the variations in the Young's modulus of the silicon strip in multiple directions of a plane by means of a modulation of the width of the strip as a function of the stresses anticipated by the strip. This solution is particularly complex to implement, because it requires knowing all the stresses expected on the strip, and adapting the shape of the strip accordingly.
European patent no 2 215 531 proposes resolving this problem by using a special silicon strip oriented in accordance with the crystallographic axis {1,1,1}, which has similar mechanical characteristics in multiple directions of a plane. This implementation requires a very special silicon that greatly constrains the process of production of the mechanical oscillator.
The technical problem addressed herein therefore consists in achieving a monocrystalline silicon mechanical oscillator that is simple to manufacture, and of which the mechanical characteristics are the same in all the directions of a plane. Furthermore, the disclosed embodiments also aim to limit the variations in mechanical characteristics as a function of temperature.